Some Novel Interactive Hybrid Weighted Aggregation Operators with Pythagorean Fuzzy Numbers and Their Applications to Decision Making

Abstract

A Pythagorean fuzzy set (PFS) is one of the extensions of the intuitionistic fuzzy set which accommodate more uncertainties to depict the fuzzy information and hence its applications are more extensive. In the modern decision-making process, aggregation operators are regarded as a useful tool for assessing the given alternatives and whose target is to integrate all the given individual evaluation values into a collective one. Motivated by these primary characteristics, the aim of the present work is to explore a group of interactive hybrid weighted aggregation operators for assembling Pythagorean fuzzy sets to deal with the decision information. The proposed aggregation operators include interactive the hybrid weighted average, interactive hybrid weighted geometric and its generalized versions. The major advantages of the proposed operators to address the decision-making problems are (i) to consider the interaction among membership and non-membership grades of the Pythagorean fuzzy numbers, (ii) it has the property of idempotency and simple computation process, and (iii) it possess an adjust parameter value and can reflect the preference of decision-makers during the decision process. Furthermore, we introduce an innovative multiple attribute decision making (MADM) process under the PFS environment based on suggested operators and illustrate with numerous numerical cases to verify it. The comparative analysis as well as advantages of the proposed framework confirms the supremacies of the method.Mathematics 2019, 7, 1150 2 of 25 that 0.4 + 0.8 > 1, so IFS cannot solve this issue, but since 0.4 2 + 0.8 2 < 1, then the PFS can easily deal with it. Therefore, in some cases, the PFS can settle a large number of problems, while the IFS cannot. Since PFS appeared, it has become a useful technique for modeling vagueness and indeterminacy of the MADM issues or multiple attribute group decision making (MAGDM) issues [5][6][7][8][9][10][11][12]. Some evaluation methods in the light of PFS are given to solve Pythagorean fuzzy MADM problems. For instance, Rani et al. [13] extended traditional TOPSIS (technique for an order of preference by similarity to ideal solution) approach to Pythagorean fuzzy numbers (PFNs) and studied the selection of a sustainable recycling partner. Considering DM's psychological characteristics, in the light of the prospect and regret theories, Peng and Dai [14] explored a stochastic decision approach under Pythagorean fuzzy setting. Ren et al. [15] extended traditional TODIM (an acronym in Portuguese of interactive and multiple attribute decision making) approach to PFNs. Chen [16] introduced a Pythagorean fuzzy VIKOR (vlseKriterijumska optimizacija I Kompromisno Resenje in Serbian) approach for MADM. Zhang [17] expanded the hierarchical QUALIFLEX (qualitative flexible multiple criteria method) algorithm to the interval-valued PFSs, and employed it to investigate the industries' risk evaluation.The way of evaluation methods in Pythagorean fuzzy decision-making problems is only one aspect, the other ...

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